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Dendritic encoding of sensory stimuli controlled bydeep cortical interneuronsMasanori Murayama1, Enrique Perez-Garci1, Thomas Nevian1, Tobias Bock1, Walter Senn1 &Matthew E. Larkum1

The computational power of single neurons is greatly enhanced byactive dendritic conductances1 that have a large influence on theirspike activity2–4. In cortical output neurons such as the largepyramidal cells of layer 5 (L5), activation of apical dendritic cal-cium channels leads to plateau potentials that increase the gain ofthe input/output function5 and switch the cell to burst-firingmode6–9. The apical dendrites are innervated by local excitatoryand inhibitory inputs as well as thalamic10–13 and corticocorticalprojections14–16, which makes it a formidable task to predict howthese inputs influence active dendritic properties in vivo. Here weinvestigate activity in populations of L5 pyramidal dendrites of thesomatosensory cortex in awake and anaesthetized rats followingsensory stimulation using a new fibre-opticmethod17 for recordingdendritic calcium changes. We show that the strength of sensorystimulation is encoded in the combined dendritic calcium responseof a local population of L5 pyramidal cells in a gradedmanner. Theslope of the stimulus–response function was under the control of aparticular subset of inhibitory neurons activatedby synaptic inputspredominantly in L5. Recordings from single apical tuft dendritesin vitro showed that activity in L5pyramidal neuronsdisynapticallycoupled via interneurons directly blocks the initiation of dendriticcalcium spikes in neighbouring pyramidal neurons. The resultsconstitute a functional description of a cortical microcircuit inawake animals that relies on the active properties of L5 pyramidaldendrites and their very high sensitivity to inhibition. The micro-circuit is organized so that local populations of apical dendrites canadaptively encode bottom-up sensory stimuli linearly across theirfull dynamic range.

To explore how dendritic activity encodes sensory input in vivo, weused a microendoscopic technique (the ‘periscope’ method17) idealfor recording from local populations of L5 pyramidal dendrites inanaesthetized and awake animals (Fig. 1a, Methods). This methodprovides calcium fluorescence signals exclusively from pyramidal api-cal tuft dendrites by combining two approaches: specific loading of L5pyramidal dendrites and horizontal imaging of the upper three layersof cortex (Fig. 1a). Fluorescence responses to sensory stimuli wererecorded from populations of L5 bolus-loaded dendrites that werenot detectable using two-photon imaging from individual dendrites18

(n5 6, data not shown; see also Methods). This method has a highsensitivity to dendritic activity and can be easily applied to awake,freely moving animals.

Air-puff stimulation of the hindlimb under urethane anaesthesiaproduced biphasic responses in dendrites of the contralateral hindlimbarea of the primary somatosensory cortex (Fig. 1b, black). This dend-ritic population response could be blocked completely by the applica-tion of the Ca21 channel blocker Cd21 to the cortical surface (Fig. 1b,grey), leaving no detectable movement artefacts. Application of theGABAA (GABA, c-aminobutyric acid) receptor antagonist, gabazine,to the cortical surface increased the first component of the dendritic

population response approximately fivefold (0.426 16% versus2.126 0.60% (all data given as mean6 s.d.), P, 0.05, n5 5; Fig. 1b,c, red), whereas the GABAB receptor antagonist CGP52432 did notchange this component (0.426 0.16% versus 0.386 0.07%, P5 0.29,n5 5; Fig. 1b, c, green). Throughout this study we focused on thefactors influencing the increase in the initial component of calciuminflux into the dendrites modulated by GABAA receptors.

We investigated the dendritic encoding of stimulus strength usingsingle electrical stimuli to the hindlimb, for which the strength couldbe reliably and precisely determined. Increasing stimulus strengthunder urethane anaesthesia resulted in a progressive increase in thepopulation dendritic calcium response (n5 21; Fig. 1d; seeSupplementary Fig. 1 for DF/F peak amplitude). Blockade of GABAreceptors dramatically increased the dendritic population response(n5 6; Fig. 1d, e, red), possibly also because of runaway corticalexcitation. Blockade of GABAB receptors alone had very little effect(n5 6; Fig. 1e, green). Normalization to the maximal dendritic res-ponse in each condition revealed that the responses to increasingstimulus strength were nearly linear under control conditions buthighly nonlinear (‘all or none’) without GABAA receptor activity(Fig. 1f).

Conscious perception involves a combination of feed-forward andfeedback processes19 that may specifically influence dendritic encod-ing. To examine dendritic sensory-evoked responses in awake ani-mals, we used a custom-built head mount to stabilize the fibre-opticcable17. As in the anaesthetized state, we found that increasing stimu-lus strength resulted in a graded increase in the population dendriticcalcium response (n5 3; Fig. 1g). This shows that the mechanismscontrolling the linear encoding of dendritic responses to sensorystimulus strength are not affected by anaesthesia. Thus, we continuedour experiments to understand in detail what neural mechanismsunderlie the change in linearity and dynamic range in anaesthetizedanimals.

We next investigated the source of dendritic Ca21. Application ofD(-)-2-amino-5-phosphonovaleric acid (APV, to block NMDAreceptors) to the cortical surface did not alter the amplitude of thedendritic population signal, indicating negligible contribution bysubthreshold Ca21 entry (that is, excitatory postsynaptic potentials(EPSPs)) as shown previously17 (P. 0.1, n5 6; Supplementary Fig.2). However, actively propagated action potentials from the somainto the apical dendrite can cause moderate increases in intracellularcalcium concentration ([Ca21]i), and dendritic Ca21 spikes cause alarge signal that is easily detectable17. There was no way to directlyestimate action potential firing with the periscope method, so wetested the contribution of back-propagating action potentials(BPAPs) to the sensory-evoked dendritic calcium signals by injectingTTX (aNa1 channel blocker) into L5 (Fig. 2a). Surprisingly, blockingactivity in L5 and preventing BPAPs did not decrease the dendriticsignal but rather increased it threefold (1.26 0.61% versus

1Physiologisches Institut, Universitat Bern, Buhlplatz 5, CH-3012 Bern, Switzerland.

doi:10.1038/nature07663

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3.36 0.95%, P, 0.05, n5 5; Fig. 2b, e) and changed the biphasicnature of the dendritic response. This result shows first that the largecalcium responses detected are dependent on neither dendriticBPAPs nor axonal action potentials and second that an additionalTTX-sensitive mechanism in L5 suppresses dendritic [Ca21]i.

Themost likely explanation is thatTTX alsoblocked some inhibitoryneurons in L5. Recent studies in vitro have shown that inhibition ofpyramidal dendrites can be evoked by activation of dendrite-targeting Martinotti interneurons by neighbouring pyramidal neu-rons20,21. To test this possibility, we suppressed the activation of thisformofdisynaptic inhibitionby local injectionofCNQX(anantagonistof a-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid (AMPA)

receptors and kainate receptors) to L5 (see also Fig. 3). Again, thecombined dendritic signal increased (0.616 0.19% versus0.996 0.36%, P, 0.05, n5 5; Fig. 2c, f). Even more importantly,blockade of both L5 activity using TTX and disynaptic connectivityusing CNQX had exactly the same effect on the slope of the dendriticresponse curve as a function of stimulus strength (Fig. 2h; seeSupplementary Fig. 3 forDF/Fpeak amplitude).We conclude that deepcortical interneurons control dendritic encoding of sensory inputs.

This conclusion was further supported by the counterintuitiveaction of gabazine when applied locally to L5, which decreased thedendritic Ca21 signal by nearly 40% (0.766 0.46% versus0.456 0.30%, P, 0.05, n5 5; Fig. 2d, g, h). This is consistent withthe hypothesis that disinhibition of L5 cells leads to an increase indendritic inhibition in the upper layers. Moreover, muscimol (aGABAA receptor agonist) application to L5 increased the signalsevoked by hindlimb stimulations (0.596 0.36% versus0.786 0.46%, P, 0.05, n5 4; Fig. 2i), whereas muscimol applica-tion to layer 1 (L1) decreased dendritic Ca21 signals (0.896 0.47%versus 0.636 0.39%, P, 0.05, n5 4; Fig. 2i). This experiment sug-gests that inhibition is mainly dendritic, not perisomatic, which wasconfirmed with muscimol in vitro (n5 3, Supplementary Fig. 4).Last, these experiments demonstrate that this form of cortical inhibi-tion predominates over increased firing in pyramidal neurons andincreases in recurrent activity.

We next investigated the mechanisms underlying inhibitory con-trol of dendritic activity. For this, we examined whether disynapti-cally evoked inhibition is sufficient to block dendritic Ca21 spikes.We performed triple-patch recordings in vitro from pairs of disynap-tically coupled L5 pyramidal neurons20 (Fig. 3a) with the thirdrecording in the dendritic Ca21 spike initiation zone 500–800 mmfrom the cell body (n5 3, Fig. 3a). Trains of 18–20 action potentialsat 80–100Hz in the presynaptic pyramidal neuron evoked disynapticdendritic inhibition (Fig. 3b). Dendritic Ca21 spikes evoked withdendritic current injection (Fig. 3c) could be completely abolishedby the disynaptically evoked dendritic inhibition in an all-or-nonefashion (Fig. 3d). The same phenomenon could be observed withcalcium imaging of the Ca21 spike initiation zone. Disynapticallyevoked inhibition severely reduced the Ca21 fluorescence due toCa21 spikes into this region evoked with high-frequency trains ofback-propagating action potentials22 (23.06 19.8%, P, 0.05, n5 3;Fig. 3e–g; for details, see Supplementary Fig. 5). The effect of disy-naptic inhibition was blocked by local application of CNQX to L5analogous to the in vivo experiments (n5 3). The strongest blockadeof inhibition occurred when CNQX was puffed close to L5 (n5 3,Fig. 3h–j), implying thatmost of the disynaptic dendritic inhibition isevoked by cells in lower cortical layers.

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population signals (relative fluorescence change, DF/F; 15 trials) recordedwith the periscope following contralateral hindlimb stimulation with an airpuff in anaesthetized rats (1mM CGP52432, 3mM gabazine and 1mMCd21applied to cortical surface). c, Summary of b (n5 5). Circles show theexperiments and bars indicate their averages. d, Top: Averaged traces (15trials) showing increase of dendritic Ca21 signals following increase incontralateral electrical stimulation (arrows indicate the stimulus timing,time-shifted for clarity) of the hindlimbwith increasing intensities (5–200V)under control conditions. Bottom: same, after blockade of all GABAreceptors. e, Summary of d (n5 21 for control, n5 6 for CGP52432 andgabazine; unpaired t-tests) fitted with sigmoidal curves with normalized datato maximal control value (200V). f, Summary of d with data normalized tomaximum in each condition (200V). g, Summary of awake experiments(n5 3). Inset, averaged traces of dendritic Ca21 signals in an awake animal.HLS, hindlimb stimulation; ROI, region of interest. *P, 0.05. Error bars,s.d.

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The experiments show that very specific cortical microcircuitry isinvolved in determining the responsiveness of apical dendrites of L5pyramidal neurons (Fig. 4a). Both the in vivo and the in vitro datasuggest that individual dendritic Ca21 signals contribute to thepopulation responses bymeans of all-or-none Ca21 spikes consistentwith previous recordings in vivo8,23, and that the inhibition of dend-ritic Ca21 spikes is also all or none24,25. To investigate how themicro-circuitry shapes the grading of the dendritic population response, wemodelled a population of two-compartment pyramidal neurons5

receiving distributed feed-forward and feedback excitation andinhibition (Fig. 4b; see Methods and Supplementary Information,model description). The distribution of Ca21 spike thresholds inthe dendritic compartments (Fig. 4c, d, green) was chosen to allowfor a steep all-or-none Ca21 population response when dendritic

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spike (Vm dend) evoked by dendritic current injection (Idend) caused a burst ofsomatic action potentials (Vm soma). d, Same as c, but with disynapticinhibition. e, Experimental diagram. Pyramidal neurons were artificiallyseparated and the putative interneuron (black) added schematically. Cell 2was filled withOGB-1 (100mM) andCa21 fluorescence (DF/F)measured at adistal ROI. CNQX (20 mM) was applied 100mm from the soma. f, Ca21

fluorescence transients (blue) were blocked by disynaptic inhibition (pink)and recovered with local application of CNQX (green). g, Summary off (n5 3). h, Experimental diagram. CNQX was applied at nine locations100mm apart in the vertical axis. i, Averaged IPSP (30 sweeps) recorded incell 2 evoked by a train of presynaptic action potentials in cell 1. j, Summaryof i (n5 3). AP, action potential. *P, 0.05. Error bars, s.d.

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Figure 2 | Deep-layer control of dendritic activity. a, Sketch showing localapplication of tetrodotoxin (TTX, 3 mM), 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX, 100mM) and gabazine (1 mM) injected into L5. b–d Averagedresponses (15 trials) in single animals. e–g, Summary of b–d (n5 5 for eachdrug). h, Responses (normalized to maximum of each condition) versusstimulus strength in control (n5 21), with TTX (n5 5), CNQX (n5 5) andgabazine (n5 5). Asterisks indicate significance with unpaired t-tests. Inset,data normalized to control. i, Summary of muscimol injection to L1 (top,n5 4) and to L5 (bottom, n5 4). Application of normal rat ringer to L5 andL1 did not change evoked Ca21 signals (0.836 0.76% for control versus0.766 0.49% for L5 and 0.776 0.46% for L1, n5 3). *P, 0.05. Error bars,s.d.

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inhibition is blocked (for example for gabazine to the cortical surface;Fig. 4c). The dendritic population response curves for the pharmaco-logical blocking experiments could be reproduced by removing thecorresponding model connectivity to upper and lower layers,respectively (Fig. 4b, c). The model also predicts that blocking thefeed-forward drive onto the inhibitoryMartinotti cells26 merely shiftsthe response curve to the left by reducing its threshold (Fig. 4d, lightblue), whereas blocking feedback inhibition20,21 increases the gain ofthe response curve and thus modulates the dynamic range of thepopulation calcium response (Fig. 4d, pink; see Supplementary Fig.11 for further details).

We conclude that the representation of sensory stimuli by corticaloutput neurons cannot be fully explained by the traditional axoso-matic integration approach, but requires active dendrites embeddedwithin highly specialized cortical microcircuitry. Dendritic activity istightly controlled by interneurons projecting from deep to upperlayers (Martinotti cells) whose function was previously unknown.We show here that these neurons dynamically modulate the slopeand threshold of the dendritic response function to match thephysiologically relevant input range.

METHODS SUMMARYFemale Wistar rats (24–40 d old) were used for these experiments. Multipledendrites of L5 pyramidal cells were loaded with a Ca21-sensitive dye, OregonGreen 488 BAPTA-1 AM (OGB-1 AM), by means of bolus injection to L5 (ref.17). Fibre-optic calcium imaging in vivo was performed in the primary somato-sensory cortex of awake and urethane-anaesthetized rats as described prev-iously17 (Fig. 1). Briefly, we used a custom-built microscope attached to afibre-optic cable (IGN-06/17, 680-mm diameter, Sumitomo ElectricIndustries). A GRIN lens, right-angled prism (5003 500mm; GrinTech) assem-bly was attached to the end of the fibre and the prism inserted into the hindlimbarea of the somatosensory cortex (determined beforehand with intrinsicimaging). Sensory responses were evoked by brief air puffs (50-ms duration)delivered to the contralateral hindlimb or a single short electrical microstimula-tion pulse (0.1-ms duration, 5–200V) through a surface electrode. All stimuliwere below the threshold for muscle responses in the hindlimb. In vitro patch-clamp recordings from L5 pyramidal cells were made in parasagittal slices pre-pared with standard techniques25. Statistical analysis was performed with pairedt-tests unless otherwise noted; asterisks denote P, 0.05.

Full Methods and any associated references are available in the online version ofthe paper at www.nature.com/nature.

Received 31 July; accepted 18 November 2008.Published online 18 January 2009.

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18. Kerr, J. N., Greenberg, D. & Helmchen, F. Imaging input and output of neocorticalnetworks in vivo. Proc. Natl Acad. Sci. USA 102, 14063–14068 (2005).

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Figure 4 | Model of microcircuitry with all-or-none dendritic Ca21 spikes.a, Diagram of cortical circuitry. The blue shaded region indicates theelements in the circuit affected by TTX, CNQX and gabazine. PC, pyramidalcell; MC, Martinotti cell; AC, aspiny cell. b, Model microcircuitry with apopulation of two-compartment pyramidal neurons with all-or-nonedendritic Ca21 events and four major classes of dendritic inputs (FFe, feed-forward excitation; FFi, feed-forward inhibition; FBe, feedback excitation;FBi, feedback inhibition; Blue and green arrows, excitation; black lines,inhibition). Dendritic feed-forward inhibition and feedback inhibition bothact through deep-layer Martinotti cells (red and blue stripes). IC, inhibitorycell. c, Data fitted with the model by mimicking the pharmacologicalblocking experiments in L5 and L1 (see Supplementary Information, modeldescription). Inset, model responses scaled to the number of neurons in thepopulation recruitable for Ca21 spikes. d, Effects of blocking feedback andfeed-forward inhibition, respectively (see text and also Supplementary Fig.10, which shows the effect of changing the strength of inhibition on theslope).

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22. Larkum, M. E., Kaiser, K. M. & Sakmann, B. Calcium electrogenesis in distal apicaldendrites of layer 5 pyramidal cells at a critical frequency of back-propagatingaction potentials. Proc. Natl Acad. Sci. USA 96, 14600–14604 (1999).

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26. Tan, Z., Hu, H., Huang, Z. J. & Agmon, A. Robust but delayed thalamocorticalactivation of dendritic-targeting inhibitory interneurons. Proc. Natl Acad. Sci. USA105, 2187–2192 (2008).

Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements We thank K. Martin, H.-R. Luscher and Y. Kudo for theircomments on themanuscript, O. Gschwend for support in the laboratory, D.Morrisfor software development, D. Limoges and J. Burkhalter for their expert technicalsupport and K. Fischer for Neurolucida reconstructions of the biocytin-filledneurons. We also thank Sumitomo Electric Industries for their generous donationof the optical fibre. This work was supported by the Swiss National ScienceFoundation (grant no. PP00A-102721/1).

Author Contributions M.M. and M.E.L. designed the study. M.M. performed theperiscope experiments in vivo, E.P.-G. performed the in vitro experiments, and T.N.and M.M. performed the in vivo two-photon experiments. W.S. and T.B. made themodel and the supplementary model description. M.M. and M.E.L. prepared themanuscript.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. Correspondence and requests for materials should beaddressed to M.E.L. (larkum@pyl.unibe.ch).

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METHODSThe following methods have already been mostly described in ref. 17.Animals and surgery. Female Wistar rats (P24–P40) were used in these experi-ments. Urethane (intraperitoneal, 1.5 g kg21) was used for experiments underanaesthesia. The head was fixed in a stereotaxic instrument (Model SR-5R,Narishige) and body temperaturemaintained at 36 to 37 uC. A craniotomy abovethe primary somatosensory cortex (33 4.4mm square), centred at 1.5mm pos-terior to bregma and 2.2mm from midline in the right hemisphere, was per-formed and the dura mater surgically removed immediately before Ca21

recording (see below). For awake experiments, the scalp was removed undergeneral anaesthesia (isoflurane, Baxter) and a local anaesthetic (lidocaine;Sigma-Aldrich) was applied to the wound. Following surgery, an analgesic wasadministered (buprenorphine (twice per day), Essex Chemie) and local anaes-thetic applied to the scalp. On the day of the experiment, a craniotomy wasperformed, a Ca21-sensitive dye was injected into L5 (see below) and a metalpost was fixed to the skull with dental cement. After anaesthesia, the animalswereretrained in a holder (Clam005, Kent Scientific).In vivo loading of Ca21-sensitive dye. Oregon Green 488 BAPTA-1 (OGB-1)AM (50mg; Molecular Probes) was mixed with 5 ml of pluronic acid (PluronicF-127, 20% solution in dimethylsulphoxide; Molecular Probes) for 15min. Thesolution was then diluted in 28 ml of HEPES-buffered solution (125mM NaCl,2.5mM KCl, 10mM HEPES) and mixed for a further 15min. The OGB-1 AMsolution was loaded into a glass pipette (tip diameter, 5–20mm) and pressure-injected into L5 (pressure, 10–25 kPa) for 1min. The pipette was withdrawn andthe area of the craniotomy was then submerged with rat ringer (135mM NaCl,5.4mM KCl, 1.8mM CaCl2, 1mM MgCl2, 5mM HEPES) for 2 h.In vivo Ca21 recording (periscope). A 100-W mercury lamp (U-LH100HG,Olympus) or a blue light-emitting-diode (LED, IBF1LS30W-3W-Slim-RX,Imac) was used as a light source. An excitation filter, a dichroic mirror, andan emission filter (as a filter set 31001, Chroma Technology) were used forepifluorescence Ca21 recordings. A 310 objective (0.45 numerical aperture,Model E58-372, Edmund Optics) was used for illuminating and imaging a fibrebundle (see below). A cooled charge-coupled-device (CCD) camera (MicroMax,Roper Scientific) was used for collecting fluorescence.A fibre bundle (IGN-06/17, Sumitomo Electric Industries) consisting of

17,000 fibre elements was used as a combined illuminating–recording fibre.The end face of the bundle was fitted with a prism-lens assembly that consistedof a right-angled prism (0.53 0.53 0.5mm; GrinTech) attached to a GRIN lens(diameter, 0.5mm; 0.5 numerical aperture; GrinTech). The working distancewas nominally 100mm and the magnification was 30.73, resulting in a field ofview of 685-mm diameter.Sensory responses were evoked by a brief air puff (50-ms duration) delivered

to the contralateral hindlimb or a single short electrical stimulation (0.1-msduration, 5–200V). Fluorescence changes were sampled at 100Hz. Data wereacquired on a personal computer using WinView software (Roper Scientific).Regions of interest were chosen offline for measuring fluorescence changes (seedata analysis section). Gabazine and CGP52432 were bought from BiotrendChemicals, tetrodotoxin (TTX) from Tocris Cookson and cadmium chloridefrom Fluka.In vivo Ca21 recording (two-photon). Two-photon excitation fluorescencemicroscopy was either performed with a femtosecond infrared laser (l5 800–810nm, 100 fs; Tsunami pumped by a Millennia VIII or Mai-Tai HP, Spectra-Physics) coupled to a laser scanning microscope (TCS SP2RS, Leica) equippedwith a340water immersionobjective (HCXAPOw40x,UVI, numerical aperture0.8) or a custom-built two-photon microscope equipped with a 320 waterimmersion objective (numerical aperture 0.95; Olympus). Excitation infrared-laser light and fluorescence-emission light were separated at 670nm (excitationfilter 670DCXXR,AHFAnalysentechnik) and the infrared lightwas blocked in thedetection pathway with an infrared-block filter (E700SP, AHF Analysentechnik).Fluorescence was detected using epifluorescence non-descanned detection.Calcium transients were recorded in line-scan mode at 500Hz from identifiedL5 tuft dendrites.

In vitro experiments. Animals were anaesthetized with a mixture of 95% CO2/5% O2 before decapitation. The brain was then rapidly transferred to ice-cold,oxygenated artificial cerebrospinal fluid (ACSF) containing 125mM NaCl,25mM NaHCO3, 2.5mM KCl, 1.25mM NaH2PO4, 1mM MgCl2, 25mM glu-cose and 2mMCaCl2 (pH 7.4). Parasagittal slices of the primary somatosensorycortex (300-mm thick) were cut with a vibrating microslicer on a block angled at15u to the horizontal and maintained at 37 uC in the preceding solution for 15–120min before use.Ca21 imaging and somatic whole-cell patch recordings of L5 neurons were

obtained with Nikon Eclipse E600FN microscopes (Nikon). Ca21 imaging wasperformed using a CCD camera (CoolSNAP, Roper Scientific). The fluorescencewas observed using standard epifluorescence filter sets for fluorescein (excitationat 480 nm; used for OGB-1) and Texas Red (Alexa 594; Molecular Probes)fluorescence (Chroma Technology). Fluorescence intensities were sampled at30–40Hz. Pipettes (4–6MV) for the whole-cell patch-clamp recordings werefilled with an intracellular solution containing 135mMK-gluconate, 7mMKCl,10mM HEPES, 10mM Na2-phosphocreatine, 4mM Mg-ATP, 0.3mM GTP,10mM Alexa 594 and 0.2% biocytin (pH 7.2 with KOH). No correction wasmade for the junction potential between the bath and pipette solutions. Therecordings were made with Multiclamp 700B (Axon Instruments), digitized at10 kHz with an analogue–digital converter (ITC-16 Instrutech) and acquired ona personal computer using Igor software (WaveMetrics). Dendritic Ca21 spikeswere evoked with EPSP-shaped current waveforms injected through a dendriticpipette: double exponential, f(t)5 (12 e{t=t1 )e{t=t2 , where t15 4ms andt25 10ms; time to peak, 5ms. Slices were perfused continuously with theACSF at 33–35 uC throughout the experiments.Data analysis. The fluorescence signals in vivowere quantified by measuring themean pixel value of amanually selected (offline) ROI for each frame of the imagestack using Igor software. Ca21 changes were expressed asDF/F5 Ft/F0, where Ftwas the average fluorescence intensity within the ROI at time t during theimaging experiment and F0 was the mean value of fluorescence intensity beforestimulation. For in vitro experiments, Ca21 changes were expressed asDF/F5 (Ft2 F0)/(F02 FB), where FB is the background fluorescence measuredfrom a region away from the recorded area.Model. The full model comprises microcircuitry with two types of inhibitoryneuron and a population of N two-compartment pyramidal neurons displayingall-or-none dendritic calcium events (0 or c). The mathematical analysis of themicrocircuitry leads to a compact description of the population calcium res-ponse, C(S), as a function of the stimulus strength, S, and the feed-forward andfeedback connection strengths bff5 FFe2 FFi and bfb5 FBe2 FBi, respectively.We fit the distribution of the calcium activation thresholds (mean, h0; standarddeviation, s) such that the steep response curve for TTX (modelled by bfb5 0) isreproduced. The population calcium response can be approximated by the sig-moidal function

C(S)<Nc

1z exp ({c(bf f log S{(h0zh1))=s)

with gain factor c5 (12 bfbc/4s)21 and threshold shift h152bfbc/2; seeSupplementary Information, model description. The pharmacological blockingexperiments are described by assuming that the corresponding model connec-tions are removed (Fig. 4b, c), and this changes the values of bff and bfb. Roughlyspeaking, these experiments lead to an increase in bfb (CNQX, TTX, gabazine toL1) with a corresponding gain increase, and to a reduction in bff (gabazine to L5)with a corresponding rightwards shift of the C(S) curve. Analogously, blockingthe feed-forward excitation of the (inhibitory) model Martinotti cells increasesbff and leads to a leftwards shift of C(S), whereas blocking the Martinotti celloutput increases bfb and leads to a gain increase (blue and pink curves in Fig. 4d).The number of pyramidal neurons, N, that can be recruited to contribute to thepopulation calcium signal is a nonlinearly increasing function of the dendriticfeedback strength bfb and a linearly increasing function of the gain factor c (seeSupplementary Information, model description).

doi:10.1038/nature07663

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